A cylindrical bucket filled with watert is whirled around in a vertical circle of radius r. What can be the minimum speed at the top of the path if water does not all out from the bucketgt? If it continues with this speed, what normal contact force the bucket exerts on water at teh lowest point of the path?

Explanation

To solve the problem step by step, we will analyze the forces acting on the water in the bucket at both the top and bottom of the vertical circular path.

### Step 1: Determine the Minimum Speed at the Top of the Path

At the top of the circular path, the forces acting on the water are:
- The gravitational force (weight) acting downwards, which is \( mg \).
- The centripetal force required to keep the water moving in a circle, which is provided by the gravitational force and the tension in the bucket.

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